Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 47 | 0 | 43 | 42 | 74 | 71 | 46 |
N.S. |
1 | 1.00 | 1.00 | 2.47 | 0.00 | 2.26 | 2.21 | 3.89 | 3.74 | 2.42 |
time (sec) |
N/A | 0.541 | 0.026 | 5.988 | 0.000 | 0.083 | 0.181 | 0.119 | 0.184 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 19 | 15 | 12 | 12 | 12 | 10 | 12 | 13 | 11 |
N.S. |
1 | 0.76 | 0.60 | 0.48 | 0.48 | 0.48 | 0.40 | 0.48 | 0.52 | 0.44 |
time (sec) |
N/A | 0.161 | 0.003 | 0.045 | 0.029 | 0.071 | 0.034 | 0.110 | 0.220 | 2.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 27 | 27 | 26 | 31 | 25 | 27 | 25 | 25 | 25 |
N.S. |
1 | 0.84 | 0.84 | 0.81 | 0.97 | 0.78 | 0.84 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.372 | 0.017 | 0.129 | 0.158 | 0.076 | 0.065 | 0.143 | 0.189 | 2.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 126 | 52 | 18 | 0 | 0 | 22 | 18 |
N.S. |
1 | 0.00 | 1.00 | 5.48 | 2.26 | 0.78 | 0.00 | 0.00 | 0.96 | 0.78 |
time (sec) |
N/A | 0.000 | 0.109 | 0.042 | 0.300 | 0.085 | 0.000 | 0.000 | 0.200 | 2.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 26 | 47 | 27 | 32 | 53 | 63 | 36 | 27 |
N.S. |
1 | 0.00 | 1.24 | 2.24 | 1.29 | 1.52 | 2.52 | 3.00 | 1.71 | 1.29 |
time (sec) |
N/A | 0.000 | 2.046 | 0.241 | 0.088 | 0.077 | 0.175 | 0.115 | 0.202 | 3.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 16 | 15 | 15 | 17 | 20 | 29 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.88 | 0.88 | 1.00 | 1.18 | 1.71 | 1.06 |
time (sec) |
N/A | 0.000 | 0.200 | 0.064 | 0.098 | 0.084 | 0.095 | 0.115 | 0.218 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 46 | 25 | 41 | 45 | 37 | 31 | 55 | 29 |
N.S. |
1 | 0.00 | 2.42 | 1.32 | 2.16 | 2.37 | 1.95 | 1.63 | 2.89 | 1.53 |
time (sec) |
N/A | 0.000 | 0.183 | 0.223 | 0.029 | 0.070 | 0.123 | 0.118 | 36.372 | 2.782 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 9 | 8 | 8 | 7 | 9 | 7 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 1.14 | 1.14 | 1.00 | 1.29 | 1.00 | 1.14 |
time (sec) |
N/A | 0.146 | 0.001 | 0.084 | 0.029 | 0.078 | 0.030 | 0.108 | 0.194 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 | 8 |
N.S. |
1 | 0.42 | 0.42 | 0.47 | 0.42 | 0.42 | 0.37 | 0.47 | 0.42 | 0.42 |
time (sec) |
N/A | 0.156 | 0.001 | 0.013 | 0.025 | 0.064 | 0.032 | 0.110 | 0.188 | 0.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 84 | 71 | 31 | 27 | 45 | 80 | 0 |
N.S. |
1 | 0.00 | 1.00 | 3.23 | 2.73 | 1.19 | 1.04 | 1.73 | 3.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.240 | 5.049 | 0.205 | 0.080 | 0.177 | 0.752 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 19 | 19 | 15 | 14 | 41 | 15 | 0 | 19 | 14 |
N.S. |
1 | 0.86 | 0.86 | 0.68 | 0.64 | 1.86 | 0.68 | 0.00 | 0.86 | 0.64 |
time (sec) |
N/A | 0.210 | 0.025 | 0.103 | 0.039 | 0.075 | 0.244 | 0.000 | 0.190 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 24 | 24 | 21 | 162 | 20 | 20 | 68 | 20 | 20 |
N.S. |
1 | 0.73 | 0.73 | 0.64 | 4.91 | 0.61 | 0.61 | 2.06 | 0.61 | 0.61 |
time (sec) |
N/A | 0.566 | 0.036 | 0.223 | 0.162 | 0.080 | 0.109 | 0.120 | 0.216 | 3.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 19 | 10 | 18 | 8 | 10 | 16 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.58 | 0.83 | 1.50 | 0.67 | 0.83 | 1.33 | 1.00 |
time (sec) |
N/A | 0.349 | 0.041 | 0.746 | 0.095 | 0.085 | 0.098 | 0.119 | 1.436 | 2.894 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 135 | 28 | 122 | 576 | 127 | 153 | 124 | 147 | 0 |
N.S. |
1 | 5.87 | 1.22 | 5.30 | 25.04 | 5.52 | 6.65 | 5.39 | 6.39 | 0.00 |
time (sec) |
N/A | 13.283 | 0.462 | 0.038 | 0.207 | 0.097 | 0.640 | 0.136 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 33 | 19 | 18 | 231 | 17 | 15 | 17 | 23 | 19 |
N.S. |
1 | 1.74 | 1.00 | 0.95 | 12.16 | 0.89 | 0.79 | 0.89 | 1.21 | 1.00 |
time (sec) |
N/A | 0.207 | 0.488 | 0.054 | 0.111 | 0.095 | 0.059 | 0.108 | 0.176 | 2.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 14 | 14 | 15 | 25 | 14 | 12 | 14 | 11 | 11 |
N.S. |
1 | 0.61 | 0.61 | 0.65 | 1.09 | 0.61 | 0.52 | 0.61 | 0.48 | 0.48 |
time (sec) |
N/A | 0.161 | 0.001 | 0.080 | 0.027 | 0.091 | 0.043 | 0.109 | 0.172 | 2.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 52 | 27 | 36 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 1.00 | 2.17 | 1.12 | 1.50 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.099 | 0.125 | 0.498 | 0.086 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 43 | 47 | 35 | 34 | 34 | 37 | 36 | 41 | 36 |
N.S. |
1 | 1.43 | 1.57 | 1.17 | 1.13 | 1.13 | 1.23 | 1.20 | 1.37 | 1.20 |
time (sec) |
N/A | 0.254 | 0.034 | 1.030 | 0.030 | 0.095 | 0.132 | 0.114 | 0.195 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 38 | 53 | 23 | 45 | 29 | 32 | 29 | 48 | 29 |
N.S. |
1 | 1.81 | 2.52 | 1.10 | 2.14 | 1.38 | 1.52 | 1.38 | 2.29 | 1.38 |
time (sec) |
N/A | 3.051 | 8.185 | 0.072 | 0.135 | 0.081 | 0.094 | 0.128 | 0.215 | 3.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 20 | 20 | 25 | 22 | 22 | 19 | 103 | 26 |
N.S. |
1 | 0.00 | 1.05 | 1.05 | 1.32 | 1.16 | 1.16 | 1.00 | 5.42 | 1.37 |
time (sec) |
N/A | 0.000 | 0.281 | 0.176 | 0.201 | 0.092 | 0.147 | 0.123 | 1.067 | 2.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 37 | 17 | 33 | 31 | 31 | 31 | 31 | 48 | 13 |
N.S. |
1 | 2.31 | 1.06 | 2.06 | 1.94 | 1.94 | 1.94 | 1.94 | 3.00 | 0.81 |
time (sec) |
N/A | 0.217 | 0.092 | 0.192 | 0.027 | 0.086 | 0.056 | 0.106 | 0.213 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 22 | 27 | 54 | 52 | 53 | 53 | 51 | 0 |
N.S. |
1 | 0.00 | 0.71 | 0.87 | 1.74 | 1.68 | 1.71 | 1.71 | 1.65 | 0.00 |
time (sec) |
N/A | 0.000 | 0.240 | 0.455 | 0.179 | 0.083 | 0.114 | 0.155 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 36 | 34 | 34 | 30 | 34 | 36 | 36 | 34 |
N.S. |
1 | 1.35 | 1.38 | 1.31 | 1.31 | 1.15 | 1.31 | 1.38 | 1.38 | 1.31 |
time (sec) |
N/A | 0.223 | 0.007 | 0.046 | 0.031 | 0.068 | 0.054 | 0.110 | 0.197 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 20 | 19 | 22 | 19 | 22 | 36 | 28 |
N.S. |
1 | 0.00 | 0.96 | 0.87 | 0.83 | 0.96 | 0.83 | 0.96 | 1.57 | 1.22 |
time (sec) |
N/A | 0.000 | 0.075 | 0.433 | 0.076 | 0.096 | 0.191 | 0.152 | 0.193 | 3.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 20 | 22 | 34 | 0 | 36 | 38 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.10 | 1.70 | 0.00 | 1.80 | 1.90 | 0.95 |
time (sec) |
N/A | 0.000 | 0.219 | 8.365 | 0.102 | 0.088 | 0.000 | 0.153 | 0.192 | 3.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 25 | 25 | 21 | 20 | 20 | 22 | 25 | 21 | 20 |
N.S. |
1 | 1.25 | 1.25 | 1.05 | 1.00 | 1.00 | 1.10 | 1.25 | 1.05 | 1.00 |
time (sec) |
N/A | 0.272 | 0.033 | 1.190 | 0.055 | 0.081 | 0.127 | 0.114 | 0.192 | 2.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 97 | 24 | 22 | 20 | 26 | 26 | 37 | 24 | 21 |
N.S. |
1 | 3.03 | 0.75 | 0.69 | 0.62 | 0.81 | 0.81 | 1.16 | 0.75 | 0.66 |
time (sec) |
N/A | 0.539 | 0.026 | 0.118 | 0.146 | 0.081 | 0.051 | 0.122 | 0.184 | 2.816 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 30 | 91 | 32 | 32 | 54 | 0 | 32 |
N.S. |
1 | 0.00 | 1.00 | 0.97 | 2.94 | 1.03 | 1.03 | 1.74 | 0.00 | 1.03 |
time (sec) |
N/A | 0.000 | 0.105 | 0.042 | 0.354 | 0.100 | 1.438 | 0.118 | 0.878 | 3.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 26 | 39 | 32 | 22 | 41 | 26 | 28 |
N.S. |
1 | 0.00 | 0.87 | 0.84 | 1.26 | 1.03 | 0.71 | 1.32 | 0.84 | 0.90 |
time (sec) |
N/A | 0.000 | 0.281 | 2.218 | 0.082 | 0.087 | 0.150 | 0.117 | 0.180 | 3.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 28 | 27 | 25 | 24 | 26 | 24 | 0 | 24 |
N.S. |
1 | 0.00 | 1.33 | 1.29 | 1.19 | 1.14 | 1.24 | 1.14 | 0.00 | 1.14 |
time (sec) |
N/A | 0.000 | 0.044 | 1.824 | 0.315 | 0.078 | 0.920 | 0.288 | 0.294 | 3.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 35 | 20 | 34 | 32 | 19 | 27 | 121 |
N.S. |
1 | 0.00 | 1.00 | 1.59 | 0.91 | 1.55 | 1.45 | 0.86 | 1.23 | 5.50 |
time (sec) |
N/A | 0.000 | 0.259 | 36.701 | 0.261 | 0.096 | 0.825 | 0.607 | 0.188 | 3.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 24 | 24 | 21 | 20 | 20 | 22 | 20 | 82 | 22 |
N.S. |
1 | 0.86 | 0.86 | 0.75 | 0.71 | 0.71 | 0.79 | 0.71 | 2.93 | 0.79 |
time (sec) |
N/A | 0.503 | 1.031 | 0.279 | 0.079 | 0.079 | 0.098 | 0.147 | 200.019 | 2.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 17 | 13 | 13 | 16 | 16 | 15 | 16 | 19 | 18 |
N.S. |
1 | 1.13 | 0.87 | 0.87 | 1.07 | 1.07 | 1.00 | 1.07 | 1.27 | 1.20 |
time (sec) |
N/A | 0.228 | 0.033 | 0.037 | 0.028 | 0.082 | 0.044 | 0.109 | 0.241 | 2.785 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 27 | 24 | 22 | 22 | 26 | 22 | 27 | 19 |
N.S. |
1 | 1.35 | 1.04 | 0.92 | 0.85 | 0.85 | 1.00 | 0.85 | 1.04 | 0.73 |
time (sec) |
N/A | 0.260 | 0.007 | 0.062 | 0.036 | 0.069 | 0.144 | 0.114 | 0.180 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | F(-1) | F | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 53 | 49 | 48 | 48 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.00 | 2.12 | 1.96 | 1.92 | 1.92 | 0.00 | 0.00 | 2.36 | 0.00 |
time (sec) |
N/A | 0.000 | 0.073 | 0.270 | 0.072 | 0.079 | 0.000 | 0.000 | 14.620 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 19 | 27 | 17 | 26 | 22 | 0 | 23 | 51 |
N.S. |
1 | 0.00 | 0.83 | 1.17 | 0.74 | 1.13 | 0.96 | 0.00 | 1.00 | 2.22 |
time (sec) |
N/A | 0.000 | 0.379 | 0.542 | 1.293 | 0.085 | 0.160 | 0.000 | 0.297 | 2.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 35 | 37 | 26 | 30 | 30 | 24 | 36 | 38 | 35 |
N.S. |
1 | 1.30 | 1.37 | 0.96 | 1.11 | 1.11 | 0.89 | 1.33 | 1.41 | 1.30 |
time (sec) |
N/A | 0.962 | 0.125 | 0.341 | 0.075 | 0.085 | 0.256 | 0.125 | 0.178 | 2.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 197 | 17 | 32 | 109 | 31 | 34 | 31 | 31 | 15 |
N.S. |
1 | 11.59 | 1.00 | 1.88 | 6.41 | 1.82 | 2.00 | 1.82 | 1.82 | 0.88 |
time (sec) |
N/A | 0.880 | 0.016 | 0.119 | 0.085 | 0.079 | 0.064 | 0.118 | 0.172 | 2.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 28 | 20 | 35 | 28 | 31 | 0 | 0 | 218 | 32 |
N.S. |
1 | 1.22 | 0.87 | 1.52 | 1.22 | 1.35 | 0.00 | 0.00 | 9.48 | 1.39 |
time (sec) |
N/A | 1.395 | 0.080 | 10.469 | 0.169 | 0.082 | 0.000 | 0.000 | 200.017 | 3.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 52 | 52 | 36 | 52 | 37 | 36 | 37 | 73 | 47 |
N.S. |
1 | 1.53 | 1.53 | 1.06 | 1.53 | 1.09 | 1.06 | 1.09 | 2.15 | 1.38 |
time (sec) |
N/A | 4.393 | 0.084 | 0.969 | 0.088 | 0.094 | 0.195 | 0.158 | 0.167 | 3.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 26 | 30 | 23 | 19 | 23 | 25 | 25 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 1.15 | 0.88 | 0.73 | 0.88 | 0.96 | 0.96 |
time (sec) |
N/A | 0.000 | 0.036 | 0.144 | 0.161 | 0.089 | 0.126 | 0.127 | 0.161 | 2.946 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | B | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 59 | 0 | 0 | 159 | 0 | 0 | 102 | 91 |
N.S. |
1 | 0.00 | 2.03 | 0.00 | 0.00 | 5.48 | 0.00 | 0.00 | 3.52 | 3.14 |
time (sec) |
N/A | 0.000 | 0.103 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.167 | 3.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 31 | 17 | 16 | 16 | 15 | 18 | 17 | 20 |
N.S. |
1 | 0.88 | 1.24 | 0.68 | 0.64 | 0.64 | 0.60 | 0.72 | 0.68 | 0.80 |
time (sec) |
N/A | 0.265 | 0.009 | 0.120 | 0.028 | 0.079 | 0.232 | 0.117 | 0.164 | 3.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 21 | 19 | 20 | 19 | 22 | 14 | 19 | 18 | 18 |
N.S. |
1 | 1.05 | 0.95 | 1.00 | 0.95 | 1.10 | 0.70 | 0.95 | 0.90 | 0.90 |
time (sec) |
N/A | 0.202 | 0.008 | 0.101 | 0.035 | 0.067 | 0.084 | 0.107 | 0.162 | 2.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 20 | 25 | 27 | 22 | 37 | 31 | 800 |
N.S. |
1 | 0.00 | 0.88 | 0.80 | 1.00 | 1.08 | 0.88 | 1.48 | 1.24 | 32.00 |
time (sec) |
N/A | 0.000 | 0.607 | 0.020 | 0.155 | 0.093 | 0.093 | 0.137 | 0.165 | 3.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 12 | 12 | 11 | 11 | 8 | 11 | 16 | 12 |
N.S. |
1 | 0.00 | 0.86 | 0.86 | 0.79 | 0.79 | 0.57 | 0.79 | 1.14 | 0.86 |
time (sec) |
N/A | 0.000 | 0.031 | 0.108 | 0.062 | 0.065 | 0.066 | 0.116 | 0.168 | 2.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 24 | 18 | 17 | 28 | 17 | 17 | 21 | 17 |
N.S. |
1 | 0.89 | 0.89 | 0.67 | 0.63 | 1.04 | 0.63 | 0.63 | 0.78 | 0.63 |
time (sec) |
N/A | 0.178 | 0.010 | 0.047 | 0.029 | 0.078 | 0.079 | 0.112 | 0.162 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 13 | 9 | 8 | 8 | 10 | 8 | 11 | 8 |
N.S. |
1 | 0.00 | 0.48 | 0.33 | 0.30 | 0.30 | 0.37 | 0.30 | 0.41 | 0.30 |
time (sec) |
N/A | 0.000 | 0.074 | 0.067 | 0.098 | 0.073 | 0.241 | 0.114 | 0.159 | 2.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 34 | 27 | 23 | 26 | 27 | 32 | 30 | 26 |
N.S. |
1 | 1.00 | 1.70 | 1.35 | 1.15 | 1.30 | 1.35 | 1.60 | 1.50 | 1.30 |
time (sec) |
N/A | 0.430 | 0.044 | 0.197 | 0.109 | 0.078 | 0.167 | 0.114 | 0.162 | 3.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 31 | 63 | 44 | 42 | 0 | 58 | 90 |
N.S. |
1 | 0.00 | 1.00 | 1.29 | 2.62 | 1.83 | 1.75 | 0.00 | 2.42 | 3.75 |
time (sec) |
N/A | 0.000 | 0.085 | 2.936 | 0.313 | 0.095 | 0.301 | 0.000 | 0.166 | 2.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | B | B | B | B |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 58 | 179 | 32 | 38 | 58 | 178 | 104 | 54 |
N.S. |
1 | 0.00 | 1.87 | 5.77 | 1.03 | 1.23 | 1.87 | 5.74 | 3.35 | 1.74 |
time (sec) |
N/A | 0.000 | 0.582 | 20.499 | 0.238 | 0.091 | 0.561 | 2.182 | 0.403 | 3.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 29 | 29 | 25 | 52 | 45 | 22 | 48 | 29 | 24 |
N.S. |
1 | 0.85 | 0.85 | 0.74 | 1.53 | 1.32 | 0.65 | 1.41 | 0.85 | 0.71 |
time (sec) |
N/A | 0.401 | 0.072 | 0.204 | 0.102 | 0.078 | 0.110 | 0.119 | 0.161 | 2.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 28 | 29 | 28 | 31 | 24 | 30 | 32 | 26 |
N.S. |
1 | 1.17 | 1.17 | 1.21 | 1.17 | 1.29 | 1.00 | 1.25 | 1.33 | 1.08 |
time (sec) |
N/A | 0.458 | 0.009 | 0.052 | 0.033 | 0.081 | 0.081 | 0.112 | 0.161 | 2.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 28 | 46 | 41 | 22 | 33 | 34 | 85 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 1.70 | 1.52 | 0.81 | 1.22 | 1.26 | 3.15 |
time (sec) |
N/A | 0.000 | 0.192 | 0.525 | 0.145 | 0.088 | 0.095 | 0.122 | 0.165 | 3.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 26 | 36 | 42 | 42 | 0 | 42 | 24 | 23 |
N.S. |
1 | 0.00 | 1.08 | 1.50 | 1.75 | 1.75 | 0.00 | 1.75 | 1.00 | 0.96 |
time (sec) |
N/A | 0.000 | 5.103 | 193.854 | 0.094 | 0.088 | 0.000 | 0.151 | 0.164 | 3.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 21 | 21 | 20 | 21 | 21 | 19 | 23 | 21 | 21 |
N.S. |
1 | 0.91 | 0.91 | 0.87 | 0.91 | 0.91 | 0.83 | 1.00 | 0.91 | 0.91 |
time (sec) |
N/A | 0.377 | 0.007 | 0.033 | 0.026 | 0.088 | 0.052 | 0.115 | 0.160 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 13 | 12 | 11 | 22 | 8 | 22 | 13 | 11 |
N.S. |
1 | 0.00 | 0.62 | 0.57 | 0.52 | 1.05 | 0.38 | 1.05 | 0.62 | 0.52 |
time (sec) |
N/A | 0.000 | 0.046 | 0.063 | 0.094 | 0.097 | 0.076 | 0.113 | 0.159 | 2.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 26 | 33 | 29 | 58 | 28 | 26 | 69 | 30 | 29 |
N.S. |
1 | 0.87 | 1.10 | 0.97 | 1.93 | 0.93 | 0.87 | 2.30 | 1.00 | 0.97 |
time (sec) |
N/A | 3.028 | 0.511 | 7.288 | 0.181 | 0.092 | 0.359 | 0.170 | 0.172 | 2.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 20 | 20 | 19 | 45 | 18 | 17 | 18 | 57 | 20 |
N.S. |
1 | 0.80 | 0.80 | 0.76 | 1.80 | 0.72 | 0.68 | 0.72 | 2.28 | 0.80 |
time (sec) |
N/A | 0.313 | 0.029 | 0.280 | 0.159 | 0.081 | 0.075 | 0.130 | 0.161 | 3.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 19 | 18 | 17 | 21 | 14 | 21 | 23 | 17 |
N.S. |
1 | 0.00 | 0.73 | 0.69 | 0.65 | 0.81 | 0.54 | 0.81 | 0.88 | 0.65 |
time (sec) |
N/A | 0.000 | 0.963 | 0.121 | 0.064 | 0.081 | 0.068 | 0.112 | 0.173 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 25 | 25 | 24 | 26 | 30 | 30 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.25 | 1.25 | 1.20 | 1.30 | 1.50 | 1.50 | 1.20 |
time (sec) |
N/A | 0.000 | 0.268 | 21.692 | 0.170 | 0.087 | 2.453 | 0.158 | 0.177 | 3.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 11 | 11 | 8 | 11 | 9 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 1.00 | 0.82 | 0.91 |
time (sec) |
N/A | 0.263 | 0.004 | 0.029 | 0.059 | 0.074 | 0.100 | 0.118 | 0.179 | 2.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 62 | 122 | 51 | 63 | 61 | 0 | 0 | 55 |
N.S. |
1 | 1.00 | 2.38 | 4.69 | 1.96 | 2.42 | 2.35 | 0.00 | 0.00 | 2.12 |
time (sec) |
N/A | 1.241 | 0.103 | 42.665 | 0.126 | 0.105 | 12.273 | 0.000 | 5.494 | 3.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 27 | 26 | 23 | 25 | 15 | 19 | 29 | 21 |
N.S. |
1 | 0.00 | 1.23 | 1.18 | 1.05 | 1.14 | 0.68 | 0.86 | 1.32 | 0.95 |
time (sec) |
N/A | 0.000 | 0.258 | 0.109 | 0.070 | 0.098 | 0.090 | 0.125 | 0.165 | 3.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 89 | 35 | 70 | 80 | 59 | 63 | 0 | 81 | 58 |
N.S. |
1 | 2.70 | 1.06 | 2.12 | 2.42 | 1.79 | 1.91 | 0.00 | 2.45 | 1.76 |
time (sec) |
N/A | 0.397 | 0.155 | 3.627 | 0.042 | 0.086 | 6.633 | 0.000 | 0.169 | 3.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | A | A | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 54 | 105 | 103 | 46 | 48 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.64 | 3.18 | 3.12 | 1.39 | 1.45 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.098 | 0.180 | 0.106 | 0.179 | 0.408 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 21 | 21 | 20 | 19 | 21 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.17 | 1.11 | 1.06 | 1.17 | 1.11 | 1.11 |
time (sec) |
N/A | 1.329 | 0.140 | 0.513 | 0.080 | 0.080 | 0.145 | 0.125 | 0.164 | 3.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 29 | 29 | 31 | 189 | 29 | 26 | 29 | 41 | 26 |
N.S. |
1 | 1.07 | 1.07 | 1.15 | 7.00 | 1.07 | 0.96 | 1.07 | 1.52 | 0.96 |
time (sec) |
N/A | 0.217 | 0.244 | 0.102 | 0.157 | 0.081 | 0.082 | 0.119 | 0.168 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 52 | 37 | 0 | 40 | 44 | 39 | 59 | 39 |
N.S. |
1 | 0.00 | 1.73 | 1.23 | 0.00 | 1.33 | 1.47 | 1.30 | 1.97 | 1.30 |
time (sec) |
N/A | 0.000 | 0.304 | 0.240 | 0.000 | 0.082 | 0.327 | 0.158 | 0.266 | 3.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 23 | 23 | 22 | 21 | 21 | 20 | 21 | 18 | 17 |
N.S. |
1 | 1.28 | 1.28 | 1.22 | 1.17 | 1.17 | 1.11 | 1.17 | 1.00 | 0.94 |
time (sec) |
N/A | 0.172 | 0.010 | 0.072 | 0.025 | 0.075 | 0.103 | 0.110 | 0.154 | 3.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 24 | 23 | 25 | 29 | 22 | 35 | 32 | 0 |
N.S. |
1 | 1.17 | 1.00 | 0.96 | 1.04 | 1.21 | 0.92 | 1.46 | 1.33 | 0.00 |
time (sec) |
N/A | 1.255 | 0.140 | 2.212 | 0.086 | 0.089 | 0.132 | 0.121 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 27 | 30 | 27 | 66 | 27 | 24 | 27 | 26 | 25 |
N.S. |
1 | 0.82 | 0.91 | 0.82 | 2.00 | 0.82 | 0.73 | 0.82 | 0.79 | 0.76 |
time (sec) |
N/A | 0.536 | 0.051 | 0.372 | 0.073 | 0.072 | 0.109 | 0.115 | 0.163 | 2.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 49 | 44 | 45 | 38 | 42 | 0 | 60 | 42 |
N.S. |
1 | 0.00 | 1.63 | 1.47 | 1.50 | 1.27 | 1.40 | 0.00 | 2.00 | 1.40 |
time (sec) |
N/A | 0.000 | 0.154 | 0.261 | 0.074 | 0.117 | 0.166 | 0.000 | 0.167 | 3.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 23 | 22 | 21 | 21 | 22 | 19 | 20 | 26 | 21 |
N.S. |
1 | 1.05 | 1.00 | 0.95 | 0.95 | 1.00 | 0.86 | 0.91 | 1.18 | 0.95 |
time (sec) |
N/A | 0.198 | 0.004 | 0.054 | 0.028 | 0.079 | 0.040 | 0.108 | 0.170 | 2.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 242 | 243 | 352 | 352 | 170 | 242 | 600 | 0 |
N.S. |
1 | 0.00 | 8.34 | 8.38 | 12.14 | 12.14 | 5.86 | 8.34 | 20.69 | 0.00 |
time (sec) |
N/A | 0.000 | 0.501 | 0.362 | 0.680 | 0.174 | 2.065 | 6.645 | 10.615 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 15 | 15 | 12 | 11 | 12 | 8 | 11 | 12 | 12 |
N.S. |
1 | 0.79 | 0.79 | 0.63 | 0.58 | 0.63 | 0.42 | 0.58 | 0.63 | 0.63 |
time (sec) |
N/A | 0.162 | 0.001 | 0.019 | 0.029 | 0.067 | 0.028 | 0.115 | 0.169 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 18 | 17 | 16 | 26 | 15 | 16 | 30 | 16 |
N.S. |
1 | 0.00 | 0.86 | 0.81 | 0.76 | 1.24 | 0.71 | 0.76 | 1.43 | 0.76 |
time (sec) |
N/A | 0.000 | 0.078 | 0.039 | 0.081 | 0.097 | 0.088 | 0.120 | 0.167 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 9 | 8 | 8 | 7 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.137 | 0.000 | 0.019 | 0.032 | 0.064 | 0.018 | 0.114 | 0.184 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 30 | 0 | 30 | 0 | 0 | 114 | 48 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.00 | 0.00 | 3.80 | 1.60 |
time (sec) |
N/A | 0.000 | 0.167 | 110.918 | 0.000 | 0.084 | 0.000 | 0.000 | 200.052 | 0.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 49 | 64 | 75 | 75 | 60 | 76 | 92 | 68 |
N.S. |
1 | 0.00 | 1.81 | 2.37 | 2.78 | 2.78 | 2.22 | 2.81 | 3.41 | 2.52 |
time (sec) |
N/A | 0.000 | 0.035 | 3.753 | 0.070 | 0.080 | 0.092 | 0.130 | 0.424 | 2.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 67 | 20 | 41 | 40 | 36 | 42 | 36 | 43 | 18 |
N.S. |
1 | 3.19 | 0.95 | 1.95 | 1.90 | 1.71 | 2.00 | 1.71 | 2.05 | 0.86 |
time (sec) |
N/A | 0.257 | 0.101 | 0.220 | 0.027 | 0.081 | 0.077 | 0.114 | 0.444 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 36 | 31 | 29 | 28 | 28 | 27 | 28 | 28 | 26 |
N.S. |
1 | 1.71 | 1.48 | 1.38 | 1.33 | 1.33 | 1.29 | 1.33 | 1.33 | 1.24 |
time (sec) |
N/A | 0.206 | 0.043 | 0.167 | 0.024 | 0.079 | 0.056 | 0.110 | 0.454 | 2.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 41 | 44 | 48 | 40 | 37 | 88 | 0 | 0 |
N.S. |
1 | 0.00 | 1.08 | 1.16 | 1.26 | 1.05 | 0.97 | 2.32 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.175 | 81.537 | 0.872 | 0.079 | 3.434 | 1.198 | 1.769 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 26 | 24 | 63 | 65 | 73 | 66 | 75 | 118 |
N.S. |
1 | 1.08 | 1.04 | 0.96 | 2.52 | 2.60 | 2.92 | 2.64 | 3.00 | 4.72 |
time (sec) |
N/A | 0.621 | 0.040 | 0.657 | 0.162 | 0.092 | 0.162 | 0.169 | 0.453 | 4.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 21 | 20 | 18 | 18 | 15 | 19 | 21 | 19 |
N.S. |
1 | 1.00 | 0.95 | 0.91 | 0.82 | 0.82 | 0.68 | 0.86 | 0.95 | 0.86 |
time (sec) |
N/A | 0.182 | 0.010 | 0.107 | 0.031 | 0.075 | 0.071 | 0.109 | 0.440 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 60 | 63 | 35 | 42 | 42 | 34 | 124 | 59 | 57 |
N.S. |
1 | 1.67 | 1.75 | 0.97 | 1.17 | 1.17 | 0.94 | 3.44 | 1.64 | 1.58 |
time (sec) |
N/A | 1.613 | 0.141 | 3.966 | 0.081 | 0.087 | 0.279 | 0.127 | 0.466 | 0.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 23 | 58 | 24 | 29 | 30 | 27 | 29 | 29 | 29 |
N.S. |
1 | 1.44 | 3.62 | 1.50 | 1.81 | 1.88 | 1.69 | 1.81 | 1.81 | 1.81 |
time (sec) |
N/A | 0.149 | 0.000 | 0.030 | 0.033 | 0.077 | 0.020 | 0.116 | 0.394 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 38 | 37 | 30 | 31 | 33 | 27 | 28 | 40 | 23 |
N.S. |
1 | 1.41 | 1.37 | 1.11 | 1.15 | 1.22 | 1.00 | 1.04 | 1.48 | 0.85 |
time (sec) |
N/A | 0.236 | 0.006 | 0.415 | 0.024 | 0.080 | 0.072 | 0.116 | 0.442 | 2.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 40 | 23 | 20 | 20 | 20 | 22 | 0 | 23 | 19 |
N.S. |
1 | 1.74 | 1.00 | 0.87 | 0.87 | 0.87 | 0.96 | 0.00 | 1.00 | 0.83 |
time (sec) |
N/A | 0.241 | 0.050 | 2.867 | 0.168 | 0.090 | 0.181 | 0.000 | 0.476 | 2.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 40 | 34 | 38 | 41 | 39 | 43 | 59 | 55 |
N.S. |
1 | 0.00 | 1.33 | 1.13 | 1.27 | 1.37 | 1.30 | 1.43 | 1.97 | 1.83 |
time (sec) |
N/A | 0.000 | 0.078 | 1.418 | 0.094 | 0.084 | 0.159 | 0.137 | 0.465 | 3.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 41 | 270 | 48 | 37 | 37 | 47 | 40 | 42 |
N.S. |
1 | 0.00 | 1.28 | 8.44 | 1.50 | 1.16 | 1.16 | 1.47 | 1.25 | 1.31 |
time (sec) |
N/A | 0.000 | 0.063 | 0.468 | 0.039 | 0.090 | 0.419 | 0.223 | 0.503 | 3.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 15 | 14 | 13 | 13 | 10 | 13 | 19 | 13 |
N.S. |
1 | 0.00 | 0.88 | 0.82 | 0.76 | 0.76 | 0.59 | 0.76 | 1.12 | 0.76 |
time (sec) |
N/A | 0.000 | 0.148 | 0.109 | 0.055 | 0.072 | 0.060 | 0.119 | 0.457 | 2.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 19 | 19 | 17 | 18 | 18 | 141 | 18 | 17 | 18 |
N.S. |
1 | 1.12 | 1.12 | 1.00 | 1.06 | 1.06 | 8.29 | 1.06 | 1.00 | 1.06 |
time (sec) |
N/A | 0.467 | 0.134 | 0.120 | 0.070 | 0.092 | 0.208 | 0.117 | 0.439 | 2.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 24 | 18 | 18 | 20 | 15 | 18 | 17 | 17 |
N.S. |
1 | 0.93 | 0.89 | 0.67 | 0.67 | 0.74 | 0.56 | 0.67 | 0.63 | 0.63 |
time (sec) |
N/A | 0.250 | 0.006 | 0.036 | 0.028 | 0.066 | 0.045 | 0.125 | 0.475 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 35 | 29 | 40 | 71 | 31 | 936 | 545 | 87 |
N.S. |
1 | 0.00 | 1.13 | 0.94 | 1.29 | 2.29 | 1.00 | 30.19 | 17.58 | 2.81 |
time (sec) |
N/A | 0.000 | 0.136 | 0.368 | 0.087 | 0.094 | 0.164 | 0.156 | 0.544 | 2.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 34 | 46 | 25 | 42 | 28 | 29 | 28 | 104 | 95 |
N.S. |
1 | 1.06 | 1.44 | 0.78 | 1.31 | 0.88 | 0.91 | 0.88 | 3.25 | 2.97 |
time (sec) |
N/A | 4.475 | 2.100 | 0.475 | 0.119 | 0.080 | 0.140 | 0.295 | 114.020 | 2.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 18 | 22 | 16 | 18 | 18 | 32 | 18 | 16 | 15 |
N.S. |
1 | 0.82 | 1.00 | 0.73 | 0.82 | 0.82 | 1.45 | 0.82 | 0.73 | 0.68 |
time (sec) |
N/A | 0.145 | 0.001 | 0.048 | 0.026 | 0.071 | 0.024 | 0.119 | 0.536 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 9 | 9 | 10 | 9 | 9 | 10 | 9 | 9 | 10 |
N.S. |
1 | 0.56 | 0.56 | 0.62 | 0.56 | 0.56 | 0.62 | 0.56 | 0.56 | 0.62 |
time (sec) |
N/A | 0.140 | 0.001 | 0.038 | 0.028 | 0.082 | 0.022 | 0.113 | 0.472 | 2.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 14593 | 2356 | 39766 | 124 | 139 | 497 | 191 | 127 |
N.S. |
1 | 0.00 | 442.21 | 71.39 | 1205.03 | 3.76 | 4.21 | 15.06 | 5.79 | 3.85 |
time (sec) |
N/A | 0.000 | 26.950 | 0.071 | 0.519 | 0.099 | 0.243 | 1.033 | 0.509 | 2.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 18 | 18 | 18 | 61 | 17 | 15 | 17 | 29 | 18 |
N.S. |
1 | 0.75 | 0.75 | 0.75 | 2.54 | 0.71 | 0.62 | 0.71 | 1.21 | 0.75 |
time (sec) |
N/A | 0.304 | 0.019 | 0.086 | 0.147 | 0.077 | 0.059 | 0.122 | 0.458 | 0.056 |